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Artist 52 [7]
3 years ago
7

Given that the hypotenuse of this right triangle is 25 cm long and that tan(Θ) = 3 Find the values of x and y, accurate to the n

earest tenth. A) x ≈ 7.9; y ≈ 23.7 B) x ≈ 23.7; y ≈ 7.9 C) x ≈ 7.9; y ≈ 26.4 D) x ≈ 26.4; y ≈ 79.1
Mathematics
2 answers:
KIM [24]3 years ago
5 0

Answer:


Step-by-step explanation:

The right triangle above you can use SOHCAHTOA and determine that tanθ =

y

x

. Replacing tanθ with 3 you get

3 =

y

x


3x = y


Then use the Pythagorean Theorem to

x2 + y2 = 252. Replace y with 3x

x2 + 9x2 = 625

10x2 = 625

x2 =

625

10


x =

25

10

= 7.9


Since,

y = 3x

y = 3(7.9) = 23.7


x ≈ 7.9; y ≈ 23.7


saveliy_v [14]3 years ago
4 0
The wording of this problem indicates that there was an illustration.  Could you possibly share that illustration?

Working without an illustration:

If tan theta = 3, then tan theta = opp/adj = 3/1.  This tells us that the opp side is 3 times as long as is the adj. side.  Let x be the shorter side, i. e., let x represent the adjacent side; then y is the longer side and represents the opposite side.

Then y = 3x (the opp side is 3x the adj side in length).

Applying the Pyth. Thm.    a^2 + b^2 = c^2,

x^2 + (3x)^2 = hyp^2 = (25 cm.)^2

So x^2 + 9x^2 = (625 cm^2)

10x^2 = 625 cm^2, or x^2 = (625 cm^2) / 10 = 62.5 cm^2

x = 7.91 cm.  Therefore, y = 3(7.91) = 23.72 cm.

We were supposed to round off these answers to the nearest 10th cm.
Therefore, x = 7.9 cm and y = 23.7 cm

Would that be A, B, C or D?
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At a recent marathon, spectators lined the street near the starting line to cheer for the runners. The crowd lined up 5 feet dee
masha68 [24]

Answer:

29568 people cheered for the runners at the start of the race

Step-by-step explanation:

From the question, the crowd lined up 5 feet deep on both sides of the street for the first mile.

This lined up crowd could be related to a rectangle that is 1 mile long and 5 feet wide.

First, Convert 1 mile to feet

1 mile = 5280 feet

Hence, the length of the rectangle is 5280 feet and the width is 5 feet.

Now, we will determine how many 5 feet by 5 feet square we can get from the 5280 feet by 5 feet rectangle. To do that, we will divide 5280 feet by 5 feet

5280 feet ÷ 5 feet = 1056

Hence, from the rectangle, we can get 1056 5 feet by 5 feet square.

From the question, you estimate that 14 people can comfortably fit in a square that measures 5 feet by 5 feet,

∴ 14 × 1056 people will comfortably fit in the crowed lined up 5 feet deep on one side of the street for the first mile.

14 × 1056 = 14784 people

This is the amount of people that will comfortably fit in the crowed lined up 5 feet deep on one side of the street for the first mile.

Since the crowd lined up on both sides of the street, then

2 × 14784 people will comfortably fit in the crowed lined up 5 feet deep on both sides of the street for the first mile

2 × 14784 = 29568 people

Hence, 29568 people cheered for the runners at the start of the race.

5 0
3 years ago
7m + 3mn when m = 8 and n = 14
Kazeer [188]

Answer:

392

Step-by-step explanation:

m = 8 and n = 14

Substituting the values of m and n in the question, we get :

7m + 3mn

=( 7 x 8) +(3 x 8 x 14)

= 56 + 336

= 392

8 0
3 years ago
Read 2 more answers
There were 200,000 animals of a certain species in 1980. Since then,this number has decreased by 4.5% each year. Approximately h
g100num [7]

Answer: Approximately 25187 animals of this species will be left in 2025

Step-by-step explanation:

We would apply the formula for exponential decay which is expressed as

y = b(1 - r)^x

Where

y represents the population of animals after x years.

x represents the number of years.

b represents the initial population of animals.

r represents rate of decay.

From the information given,

b = 200000

r = 4.5% = 4.5/100 = 0.045

x = 2025 - 1980 = 45 years

Therefore,

y = 200000(1 - 0.045)^45

y = 200000(0.955)^45

y = 25187

8 0
3 years ago
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If x^3 times x^b equals x^15, which could be a correct value for "b?"
crimeas [40]
B=5
Hope this helps!
Vote me brainliest!
4 0
3 years ago
What is the distance between the following points?
Elenna [48]

Answer:

11

Step-by-step explanation:

there are 11 spaces between the points

just count the number of spaces, no calculations needed.

6 0
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